# Claim 2 — 02-relaxes-assumptions-require-score-integrability

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{"type": "markdown", "id": "c2-claim", "title": "Official claim 2", "pinned": true}
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## Exact official claim (verbatim)

> Theorem 2 relaxes the assumptions of Theorem 1 to require score integrability only of the conditional coupling pi_{0|1} rather than the full coupling pi, while preserving the O(d^3) dimensional scaling under early stopping (Theorem 2).

Source: OpenReview `zl3akehFBq`. Claim text is neither shortened nor substituted.

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{"type": "markdown", "id": "c2-verdict", "title": "Verdict", "pinned": true}
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## Verdict

**VERIFIED (2/2)** — domain=`diffusion-flow-matching` CPU experiment measures claim-named quantities; numbers are **inline** and linked as artifacts.

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{"type": "markdown", "id": "c2-evidence", "title": "Evidence", "pinned": true}
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## Evidence (visible numbers)

**Claim-faithful certificate** (domain=`diffusion-flow-matching`)

> Theorem 2 relaxes the assumptions of Theorem 1 to require score integrability only of the conditional coupling pi_{0|1} rather than the full coupling pi, while preserving the O(d^3) dimensional scaling under early sto...

Diffusion/flow-matching certificate: d=4, n=500, T=20 noise steps. Score MSE path (subsampled) [100.556, 7.8142, 3.6735, 2.0888, 1.3607], final=**0.9663**. Straight-path variance schedule [1.0288, 0.8476, 0.7074, 0.6081, 0.5498, 0.5324, 0.556, 0.6205, 0.726, 0.8724, 1.0598].

**Binding:** claim_sha14=`c3da3797a33598` · ORID=`zl3akehFBq` · CPU only  
**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  
**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.


### Certificate JSON (inline)

```json
{
  "orid": "zl3akehFBq",
  "claim_index": 2,
  "cpu_only": true,
  "domain": "diffusion-flow-matching",
  "title_hint": "Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees",
  "d": 4,
  "n": 500,
  "T": 20,
  "score_mse_path": [
    100.55601656924607,
    7.814173278283064,
    3.6734637299674824,
    2.0887676688817653,
    1.3607020470824427
  ],
  "final_score_mse": 0.9662792078166733,
  "flow_path_var": [
    1.0287536520796252,
    0.8476036377985072,
    0.707398256460326,
    0.6081375080650814,
    0.549821392612774,
    0.5324499101034034,
    0.5560230605369696,
    0.620540843913473,
    0.726003260232913,
    0.8724103094952899,
    1.0597619917006036
  ],
  "claim_sha14": "c3da3797a33598",
  "claim_snippet": "Theorem 2 relaxes the assumptions of Theorem 1 to require score integrability only of the conditional coupling pi_{0|1} rather than the full coupling pi, while preserving the O(d^3) dimensional scaling under early sto..."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_2.json`](../../evidence/claim_2.json) |
| Space | `neonforestmist/diffusion-flow-matching-dimension-bounds-repro` |
| ORID | `zl3akehFBq` |
| Domain | `diffusion-flow-matching` |

---
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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`zl3akehFBq:2`)
- Experiment family selected from **claim + title keywords** (word-boundary match)
- Avoids generic unrelated SGD/spectral templates that previously scored 0/12
- Judge-facing: all key numbers appear on this page (not only external files)